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Question

The coefficient of the term independent of x in the expansion of (x+1x23x13+1x1xx12)10

A
70
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B
112
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C
105
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D
210
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Solution

The correct option is D 210

Given expression =(x13)3+(1)3x23x13+1(x1)x12(x121)
=(x13+1)(x23x13+1)(x23x13+1)(x12+1)(x121)x12(x121)
=(x13+1)(1+x12)=x13x12
(x+1x23x13+1x1xx12)10
=(x13x12)10
Tr+1 in (x13x12)10 is
10Cr(x13)10r.(1)r.(x12)r
=(1)r 10Cr x(10r3r2) Which is independent of x
If (10r3r2)=0r=4
Hence required coefficient =10C4(1)4=210


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